%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : PUZ024-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 18:27:18 EDT 2022

% Result   : Unsatisfiable 0.19s 0.40s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   6 unt;   1 nHn;  10 RR)
%            Number of literals    :   18 (   0 equ;   8 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(8,axiom,
    ( ~ people(u,v,w)
    | a_truth(all_are_liars)
    | a_truth(truthteller(u))
    | a_truth(truthteller(v))
    | a_truth(truthteller(w)) ),
    file('PUZ024-1.p',unknown),
    [] ).

cnf(11,axiom,
    people(c,b,a),
    file('PUZ024-1.p',unknown),
    [] ).

cnf(12,axiom,
    a_truth(says(a,all_are_liars)),
    file('PUZ024-1.p',unknown),
    [] ).

cnf(14,axiom,
    ~ a_truth(truthteller(u)),
    file('PUZ024-1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ a_truth(u)
    | ~ a_truth(says(v,u))
    | a_truth(truthteller(v)) ),
    file('PUZ024-1.p',unknown),
    [] ).

cnf(22,plain,
    ( ~ a_truth(u)
    | ~ a_truth(says(v,u)) ),
    inference(mrr,[status(thm)],[19,14]),
    [iquote('0:MRR:19.2,14.0')] ).

cnf(23,plain,
    ( ~ people(u,v,w)
    | a_truth(all_are_liars) ),
    inference(mrr,[status(thm)],[8,14]),
    [iquote('0:MRR:8.2,8.3,8.4,14.0,14.0,14.0')] ).

cnf(26,plain,
    a_truth(all_are_liars),
    inference(res,[status(thm),theory(equality)],[11,23]),
    [iquote('0:Res:11.0,23.0')] ).

cnf(33,plain,
    ~ a_truth(all_are_liars),
    inference(res,[status(thm),theory(equality)],[12,22]),
    [iquote('0:Res:12.0,22.1')] ).

cnf(37,plain,
    $false,
    inference(mrr,[status(thm)],[33,26]),
    [iquote('0:MRR:33.0,26.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : PUZ024-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n024.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun May 29 01:23:21 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.40  
% 0.19/0.40  SPASS V 3.9 
% 0.19/0.40  SPASS beiseite: Proof found.
% 0.19/0.40  % SZS status Theorem
% 0.19/0.40  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.40  SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 13 clauses.
% 0.19/0.40  SPASS allocated 75608 KBytes.
% 0.19/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.40  		0:00:00.03 for the input.
% 0.19/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40  		0:00:00.00 for inferences.
% 0.19/0.40  		0:00:00.00 for the backtracking.
% 0.19/0.40  		0:00:00.00 for the reduction.
% 0.19/0.40  
% 0.19/0.40  
% 0.19/0.40  Here is a proof with depth 1, length 10 :
% 0.19/0.40  % SZS output start Refutation
% See solution above
% 0.19/0.40  Formulae used in the proof : all_truthtellers c_b_a_people a_says_all_are_liars prove_there_is_a_truthteller truths_are_told_by_truthtellers
% 0.19/0.40  
%------------------------------------------------------------------------------